I spent one more night trying to figure this out, and I did it!

My amended Federal return was E-filed and accepted yesterday!

Note:  In the file that you are preparing the amended Form 1040X, very important --

DO NOT UNCLICK the BOX that was checked originally as E-file Federal and State returns.

You have to leave these boxes checked, and also check the BOX to "E-file the Amended Return".

If you unclick the BOX that was checked originally as E-file (which I did initially because it made sense to me to unclick this), the software will not recognize that the original return was E-filed.